Given $$ a0,b0,c0 $$ , prove $$ a^2+b^2+c^2-ab-bc-ac≥0 $$

Question

Given $$ a>0,b>0,c>0 $$ , prove $$ a^2+b^2+c^2-ab-bc-ac≥0 $$

Uniteasy Admin · Accepted Answer

$$ a^2+b^2+c^2-ab-bc-ac $$
$$ =\dfrac{1}{2} (2a^2+2b^2+c^2-2ab-2bc-2ac) $$
$$ =\dfrac{1}{2} [(a-b)^2+(b-c)^2+(a-c)^2] $$
$$ ≥0 $$